Strategy-Free criterion

Contents

Definitions

A sincere vote is one with no falsified preferences or preferences left unspecified when the election method allows them to be specified (in addition to the preferences already specified).

One candidate is preferred over another candidate if, in a one-on-one competition, more voters prefer the first candidate than prefer the other candidate.

If one candidate is preferred over each of the other candidates, that candidate is called "Condorcet candidate" or "Condorcet winner".

Statement of Criterion

If a Condorcet candidate exists, and if a majority prefers this candidate to another candidate, then the other candidate should not win if that majority votes sincerely and no other voter falsifies
any preferences.

In a ranked method, it is nearly equivalent to say: If more than half of the voters rank x above y, and there is no candidate z whom more than half of the voters rank above x, then y must not be elected.

Complying Methods

Commentary

The reader may be wondering how the Condorcet candidate, if one exists, could
possibly not be preferred by a majority of voters over any
other candidate. The key is that some voters may have no preference
between a given pair of candidates. Out of 100 voters, for example, 45
could prefer the Condorcet candidate over another particular candidate, and 40 could
prefer the opposite, with the other 15 having no preference between the
two. In that case, it is not true that a majority of voters prefer the
Condorcet candidate over the other candidate, and SFC does not apply.

In order to understand SFC, one must also understand that there are
two types of insincere votes: false preferences and truncated
preferences. Voters truncate by terminating their rank list
before their true preferences are fully specified (note that the last
choice is always implied, so leaving it out is not considered
truncation). Voters falsify their preferences, on the other
hand, by reversing the order of their true preferences or by specifying
a preference they don't really have. Suppose, for example, that a
voter's true preferences are (A,B,C) with no preference between D and E.
The vote (A) or (A,B) would be a truncated vote, and the vote (B,A,C) or (A,C,B)
or (A,B,C,D,E) would be a falsified vote.

SFC requires that the majority of voters who prefer the Condorcet candidate to
another particular candidate vote sincerely (neither falsify nor
truncate their preferences), and it also requires that no other voter
falsifies preferences. SFC therefore implies that the minority that does
not prefer the Condorcet candidate to the other candidate cannot cause the other
candidate to win by truncating their preferences. (In theory, that
minority could cause the other candidate to win by falsifying their
preferences, but that would be a very risky offensive strategy
that is more likely to backfire than to succeed.) The significance of
the SFC guarantee is that the majority has no need for defensive
strategy, hence the name Strategy-Free Criterion.

Schulze was shown to comply with both the
Condorcet and Generalized Condorcet Criteria (CC and GCC) above.
Although compliance with CC and GCC are important, those criteria apply
only in the theoretically ideal case in which all votes are sincere. The
Strategy-Free criterion goes further and shows that, under certain
reasonable conditions, a majority of voters have no incentive to vote
insincerely. The fact that Schulze also complies with SFC
therefore enhances the significance of CC and GCC considerably.